The state Supreme Court last week rejected Larry Eugene Mann's appeal, TBO.com, Tampa, reported.
In that appeal, Mann's attorney argued he shouldn't be executed because the jury wasn't unanimous in recommending the death penalty.
On Monday, the lawyers told the U.S. Supreme Court Mann's constitutional rights had been infringed because Gov. Rick Scott had signed his death warrant in a secret process that lacked standards.
He is scheduled to die by lethal injection at 6 p.m. Monday for killing Elisa Nelson as she rode her bicycle to school Nov. 4, 1980, the Tampa Bay (Fla.) Times reported.
Mann has never denied kidnapping the girl in Palm Harbor, about 20 miles north of St. Petersburg, nor has he denied taking her to the orange grove where her body was later found.
In his appeal to the Florida high court, Mann said he was not the violent predator he used to be. He noted his spotless prison record, the respect both inmates and guards had for him, and his studies of the Bible.
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